Find all the intersection points of the following two circles: -

Ausanioyck 2022-03-03 Answered
Find all the intersection points of the following two circles:
- The center circle (0,0) And its radius 13
- The center circle (1, -1) And its radius 17
(Note: Write the answer as follows (x1,y1)(x2,y2))
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Expert Answer

Clay Giles
Answered 2022-03-04 Author has 4 answers

Let the equation of circle is
(xh)2+(yk)2=r2
Where, h and k are the x and y coordinates of the center of the circle.
And r is the radius of the circle.
Find the equation of circles by given information,
(x0)2+(y0)2=(13)2
x2+y2=13
x2+y213=0 (1)
(x1)2+(y(1))2=(17)2
(x1)2+(y+1)2=17
x2+12x+y2+1+2y=17
x2+12x+y2+1+2y17=0 (2)
Multiply equation (1) by -1 and add both the equation:
x2y2+13=0
After adding:
12x+1+2y4=0
2x+2y2=0
x+y1=0
y=x+1
Substitute the value of y in equation (1),
x2+y213=0
x2+(x+1)213=0
x2+x2+1+2x13=0
2x2+2x12=0
x2+x6=0
x2+3x2x6=0
x2+3x2x6=0
x(x+3)2(x+3)=0
(x+3)(x2)=0
x=3,2
x1=3,x2=2
y1=3+1
y1=2
y2=2+1
y2=3

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